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Worksheet: Dividing Polynomials by a Divisor of First Degree with No Remainder

In this worksheet, we will practice dividing polynomials using an algorithm similar to that of long division of integers with no remainder.

Q1:

Knowing that the length of a rectangle is 3 π‘₯ βˆ’ 4 and its area is 6 π‘₯ βˆ’ 8 π‘₯ + 9 π‘₯ βˆ’ 9 π‘₯ βˆ’ 4 4 3 2 , express the width of the rectangle as a polynomial in standard form.

  • A 2 π‘₯ + 3 π‘₯ βˆ’ 1 3
  • B 3 π‘₯ + 2 π‘₯ + 1 3
  • C 3 π‘₯ + 2 π‘₯ βˆ’ 1 3
  • D 2 π‘₯ + 3 π‘₯ + 1 3
  • E π‘₯ + 3 π‘₯ + 2 3

Q2:

The expression 4 𝑦 + 8 𝑦 βˆ’ 5 2 has two factors. One factor is ( 2 𝑦 + 5 ) , what is the other factor?

  • A ( 3 𝑦 βˆ’ 1 )
  • B ( 2 𝑦 + 1 )
  • C ( 2 𝑦 + 2 )
  • D ( 2 𝑦 βˆ’ 1 )
  • E ( 2 𝑦 βˆ’ 2 )

Q3:

Find the value of π‘Ž given that 6 π‘₯ + π‘Ž π‘₯ βˆ’ 3 0 π‘₯ βˆ’ 2 1 π‘₯ + 1 0 4 3 2 is divisible by ( 2 π‘₯ + 5 ) .

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